Tail sums of Wishart and Gaussian eigenvalues beyond the bulk edge

Tail sums of Wishart and Gaussian eigenvalues beyond the bulk edge Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits of large N and n, with positive ratio γ in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of γ. These statements are consequences of quantitative bounds on tail sums of eigenvalues outside the bulk which are established here for applications in high dimensional covariance matrix estimation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Australian & New Zealand Journal of Statistics Wiley

Tail sums of Wishart and Gaussian eigenvalues beyond the bulk edge

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Publisher
Wiley
Copyright
Copyright © 2018 Australian Statistical Publishing Association Inc.
ISSN
1369-1473
eISSN
1467-842X
D.O.I.
10.1111/anzs.12201
Publisher site
See Article on Publisher Site

Abstract

Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits of large N and n, with positive ratio γ in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of γ. These statements are consequences of quantitative bounds on tail sums of eigenvalues outside the bulk which are established here for applications in high dimensional covariance matrix estimation.

Journal

Australian & New Zealand Journal of StatisticsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ;

References

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